메뉴 건너뛰기




Volumn 64, Issue 11, 2006, Pages 2400-2411

Strong convergence of the CQ method for fixed point iteration processes

Author keywords

CQ method; Maximal monotone operator; Nonexpansive mapping; Strong convergence

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; MAPPING; THEOREM PROVING;

EID: 33644950086     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2005.08.018     Document Type: Article
Times cited : (382)

References (26)
  • 2
    • 1342265919 scopus 로고    scopus 로고
    • A unified treatment of some iterative algorithms in signal processing and image reconstruction
    • C. Byrne A unified treatment of some iterative algorithms in signal processing and image reconstruction Inverse Problems 20 2004 103 120
    • (2004) Inverse Problems , vol.20 , pp. 103-120
    • Byrne, C.1
  • 3
    • 23044526412 scopus 로고    scopus 로고
    • An example on the Mann iteration method for Lipschitz pseudocontractions
    • C.E. Chidume, and S.A. Mutangadura An example on the Mann iteration method for Lipschitz pseudocontractions Proc. Am. Math. Soc. 129 2001 2359 2363
    • (2001) Proc. Am. Math. Soc. , vol.129 , pp. 2359-2363
    • Chidume, C.E.1    Mutangadura, S.A.2
  • 4
    • 51249189005 scopus 로고
    • An example concerning fixed points
    • A. Genel, and J. Lindenstrass An example concerning fixed points Israel J. Math. 22 1975 81 86
    • (1975) Israel J. Math. , vol.22 , pp. 81-86
    • Genel, A.1    Lindenstrass, J.2
  • 5
    • 0003263852 scopus 로고
    • Topics in metric fixed point theory
    • Cambridge University Press, Cambridge
    • K. Goebel, W.A. Kirk, Topics in Metric Fixed Point Theory, Cambridge Studies in Advanced Mathematics, vol. 28, Cambridge University Press, Cambridge, 1990.
    • (1990) Cambridge Studies in Advanced Mathematics , vol.28
    • Goebel, K.1    Kirk, W.A.2
  • 6
    • 0026123473 scopus 로고
    • On the convergence of the proximal point algorithm for convex optimization
    • O. Güler On the convergence of the proximal point algorithm for convex optimization SIAM J. Control Optim. 29 1991 403 419
    • (1991) SIAM J. Control Optim. , vol.29 , pp. 403-419
    • Güler, O.1
  • 7
    • 84894234564 scopus 로고
    • Fixed points of nonexpanding maps
    • B. Halpern Fixed points of nonexpanding maps Bull. Am. Math. Soc. 73 1967 957 961
    • (1967) Bull. Am. Math. Soc. , vol.73 , pp. 957-961
    • Halpern, B.1
  • 8
    • 84968476637 scopus 로고
    • Fixed points by a new iteration method
    • S. Ishikawa Fixed points by a new iteration method Proc. Am. Math. Soc. 44 1974 147 150
    • (1974) Proc. Am. Math. Soc. , vol.44 , pp. 147-150
    • Ishikawa, S.1
  • 9
    • 0041657484 scopus 로고    scopus 로고
    • Strong convergence of a proximal-type algorithm in a Banach space
    • S. Kamimura, and W. Takahashi Strong convergence of a proximal-type algorithm in a Banach space SIAM J. Optim. 13 2003 938 945
    • (2003) SIAM J. Optim. , vol.13 , pp. 938-945
    • Kamimura, S.1    Takahashi, W.2
  • 10
    • 14544304518 scopus 로고    scopus 로고
    • Strong convergence of modified Mann iterations
    • T. Kim, and H.K. Xu Strong convergence of modified Mann iterations Nonlinear Anal. 61 2005 51 60
    • (2005) Nonlinear Anal. , vol.61 , pp. 51-60
    • Kim, T.1    Xu, H.K.2
  • 11
    • 30144434356 scopus 로고    scopus 로고
    • Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups
    • this issue, doi:10.1016/j.na.2005.05.059
    • T. Kim, H.K. Xu, Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal., this issue, doi:10.1016/j.na.2005.05.059.
    • Nonlinear Anal.
    • Kim, T.1    Xu, H.K.2
  • 12
    • 0000736340 scopus 로고
    • Approximation de points fixes de contractions
    • P.L. Lions Approximation de points fixes de contractions C.R. Acad. Sci. Sr. A-B Paris 284 1977 1357 1359
    • (1977) C.R. Acad. Sci. Sr. A-B Paris , vol.284 , pp. 1357-1359
    • Lions, P.L.1
  • 13
    • 84968518052 scopus 로고
    • Mean value methods in iteration
    • W.R. Mann Mean value methods in iteration Proc. Amer. Math. Soc. 4 1953 506 510
    • (1953) Proc. Amer. Math. Soc. , vol.4 , pp. 506-510
    • Mann, W.R.1
  • 14
    • 24944447156 scopus 로고    scopus 로고
    • Convergence of generalized proximal point algorithms
    • G. Marino, and H.K. Xu Convergence of generalized proximal point algorithms Comm. Appl. Anal. 3 2004 791 808
    • (2004) Comm. Appl. Anal. , vol.3 , pp. 791-808
    • Marino, G.1    Xu, H.K.2
  • 15
    • 0037845289 scopus 로고    scopus 로고
    • Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups
    • K. Nakajo, and W. Takahashi Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups J. Math. Anal. Appl. 279 2003 372 379
    • (2003) J. Math. Anal. Appl. , vol.279 , pp. 372-379
    • Nakajo, K.1    Takahashi, W.2
  • 16
    • 0001720708 scopus 로고
    • Weak convergence theorems for nonexpansive mappings in Banach spaces
    • S. Reich Weak convergence theorems for nonexpansive mappings in Banach spaces J. Math. Anal. Appl. 67 1979 274 276
    • (1979) J. Math. Anal. Appl. , vol.67 , pp. 274-276
    • Reich, S.1
  • 17
    • 33745998912 scopus 로고
    • Strong convergence theorems for resolvents of accretive operators in Banach spaces
    • S. Reich Strong convergence theorems for resolvents of accretive operators in Banach spaces J. Math. Anal. Appl. 75 1980 287 292
    • (1980) J. Math. Anal. Appl. , vol.75 , pp. 287-292
    • Reich, S.1
  • 18
    • 0016985417 scopus 로고
    • Monotone operators and the proximal point algorithm
    • R.T. Rockafellar Monotone operators and the proximal point algorithm SIAM J. Control Optim. 14 1976 877 898
    • (1976) SIAM J. Control Optim. , vol.14 , pp. 877-898
    • Rockafellar, R.T.1
  • 19
    • 84971791384 scopus 로고
    • Weak and strong convergence to fixed points of asymptotically nonexpansive mappings
    • J. Schu Weak and strong convergence to fixed points of asymptotically nonexpansive mappings Bull. Austral. Math. Soc. 43 1991 153 159
    • (1991) Bull. Austral. Math. Soc. , vol.43 , pp. 153-159
    • Schu, J.1
  • 20
    • 21944452074 scopus 로고    scopus 로고
    • Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces
    • N. Shioji, and W. Takahashi Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces Proc. Am. Math. Soc. 125 1997 3641 3645
    • (1997) Proc. Am. Math. Soc. , vol.125 , pp. 3641-3645
    • Shioji, N.1    Takahashi, W.2
  • 21
    • 0001279962 scopus 로고    scopus 로고
    • Forcing strong convergence of proximal point iterations in a Hilbert space
    • M.V. Solodov, and B.F. Svaiter Forcing strong convergence of proximal point iterations in a Hilbert space Math. Programming Ser. A 87 2000 189 202
    • (2000) Math. Programming Ser. A , vol.87 , pp. 189-202
    • Solodov, M.V.1    Svaiter, B.F.2
  • 22
    • 0001057714 scopus 로고
    • Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process
    • K.K. Tan, and H.K. Xu Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process J. Math. Anal. Appl. 178 2 1993 301 308
    • (1993) J. Math. Anal. Appl. , vol.178 , Issue.2 , pp. 301-308
    • Tan, K.K.1    Xu, H.K.2
  • 23
    • 84966202384 scopus 로고
    • Fixed point iteration processes for asymptotically nonexpansive mappings
    • K.K. Tan, and H.K. Xu Fixed point iteration processes for asymptotically nonexpansive mappings Proc. Am. Math. Soc. 122 1994 733 739
    • (1994) Proc. Am. Math. Soc. , vol.122 , pp. 733-739
    • Tan, K.K.1    Xu, H.K.2
  • 24
    • 0001682125 scopus 로고
    • Approximation of fixed points of nonexpansive mappings
    • R. Wittmann Approximation of fixed points of nonexpansive mappings Arch. Math. 58 1992 486 491
    • (1992) Arch. Math. , vol.58 , pp. 486-491
    • Wittmann, R.1
  • 25
    • 0036692463 scopus 로고    scopus 로고
    • Iterative algorithms for nonlinear operators
    • H.K. Xu Iterative algorithms for nonlinear operators J. London Math. Soc. 66 2002 240 256
    • (2002) J. London Math. Soc. , vol.66 , pp. 240-256
    • Xu, H.K.1
  • 26
    • 28044435466 scopus 로고    scopus 로고
    • Remarks on an iterative method for nonexpansive mappings
    • H.K. Xu Remarks on an iterative method for nonexpansive mappings Comm. Appl. Nonlinear Anal. 10 1 2003 67 75
    • (2003) Comm. Appl. Nonlinear Anal. , vol.10 , Issue.1 , pp. 67-75
    • Xu, H.K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.